Fractions and Decimals


Fractions have been used for thousands of years.
"A fraction (from the Latin fractus, broken) is a number that can represent part of a whole.
The earliest fractions were ... symbols representing one half, one third, one quarter, and so on. A much later development were the common or "vulgar" fractions which are still used today, and which consist of a numerator and a denominator, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole. An example is 3/4, in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole."Wikipeadia
The Babylonian (an ancient empire) counting system used the number 60 as its base. 60 is an easy number to break into simple fractions; 1/2 (30mins.), 1/3 (20mins.), 1/4 (15mins.), 1/5 (6mins.) and 1/6 (5mins.). We use this system to tell time.

"The decimal (base ten or occasionally denary) numeral system has ten as its base. It is the most widely used numeral system. Ten is the number which is the count of fingers and thumbs on both hands (or toes on the feet). In many languages the word digit or its translation is also the anatomical term referring to fingers and toes.
Examples (of base ten systems) are Roman numerals, Brahmi numerals, and Chinese numerals, as well as the Hindu-Arabic numerals used by speakers of English. Roman numerals have symbols for the decimal powers (1, 10, 100, 1000) and secondary symbols for half these values (5, 50, 500). Brahmi numerals had symbols for the nine numbers 1–9, the nine decades 10–90, plus a symbol for 100 and another for 1000. Chinese has symbols for 1–9, and fourteen additional symbols for higher powers of 10, which in modern usage reach 1044."Wikipeadia
external image John_Napier.jpgIn 1616 John Napier, a Scottish mathematician, suggested using a decimal point to show numbers that contain a whole number and a fractional part. The digits to the left of the decimal point represent the whole number (and 0); the numbers on the right of the decimal show the fractional part.




1. Fractions vs. Decimals: What do You Think?

Decimals are used in measurement, money and on calculators, while fractions seem to be used more in every day conversations.
"It's half-time at the big match.'
"A third of the class were away sick today."
"I'll meet you there at quarter to."
  • Your first task is to create a comparison matrix to explore, compare and contrast the various strengths and weaknesses of fractions and decimals (yes Gab you can include percentages if you want).



Finished Work
(follow the links)
Gabriel and Jacob
Alec
Jim and Jake


2. Fraction Fiction

  • Your second task is to create a story illustrating the way fractions work. Below you'll find two examples to demonstrate. Please use these as examples and not as templates.

Sixteen people are about to make a journey. They are all asked to meet at 8:00 a.m. at a designated place. By 8:05 only four have turned up. This is four sixteenths or one quarter. It was decided to travel in four cars so one car set off. That left twelve people to arrive. By 8:15 three had arrived, or one quarter of the remaining number. This meant that one twelfth or one sixteenth of the original part would have come before half of the agreed total of cars could leave.

Jennifer and Dave set out on a 520 kilometre journey to take their vacation. They expected it would take about six hour driving. They started at 2:00 p.m. By 3:30 (which was a quarter of the time altered), they travelled only 120 kilometres or two ninths of there journey. They decided to try and do another third (or 180 kilometres) in another hour and a half. This would mean that they had come five ninths of the way with only a third of the time they had anticipated spending left.

Click to see our completed Fraction Fiction stories


3. Students Got Game


  • Your third task is to design an online game based around fractions, decimals or percentages. On the Maths Websites page you'll find links to many such games. As a starting point think about their strengths and weaknesses. How well do they get the knowledge across? Can games help achieve learning goals? Are they all about the learning or are they simply about the play? What is it that you wish to communicate about fractions, decimals or percentages?

You will design and make the game, and record your thinking and working processes to place onto this wiki.
You must test your game and reflect on how it meets the mathematical needs of the players. This reflection and your self reflection will also go on this wiki.

On your own page you need to include:
1. The name of your game
2. The maths concept your game is reinforcing.
3. The rules of your game.
4. A description of the game including all the parts and elements.
5. Your reflection of the game after testing it.
6. How your game could be further developed or improved.
7. Personal reflections of the task as a whole.

For an example of how students at another school (year 7s) completed a similar task go to http://bbimathex.wikispaces.com/Design+a+game+task and click on the student's names at the bottom of the page.

Finished Work (follow the links)
Gabriel
Jacob
Alec

Jim and Jake